求解 =1.23*10^-100/789+

$$= \frac { 1.23 \times 10 ^ { - 100 } } { 789 } +$$

求值

$$\frac{41}{263000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 1.558935361 \cdot 10^{-103}$$

求解步骤

计算 -100 的 10 乘方，得到 \frac{1}{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{1.23\times \frac{1}{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{789}$$

将 1.23 与 \frac{1}{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{123}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{\frac{123}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{789}$$

将 \frac{\frac{123}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{789} 化为简分数。

$$\frac{123}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times 789}$$

将 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 与 789 相乘，得到 789000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000。

$$\frac{123}{789000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

通过求根和消去 3，将分数 \frac{123}{789000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 降低为最简分数。

$$\frac{41}{263000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{41}{263 \cdot 2 ^ {102} \cdot 5 ^ {102}} = 1.5589353612167303 \times 10^{-103}$$